y=-(x+7)^2-9

Question

y=-(x+7)^2-9

Bytelearn · Accepted Answer

Identify function: Identify the function to differentiate. We are given the function y = -(x+7)^2 - 9, and we need to find its derivative with respect to x.Apply chain rule: Apply the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is -u^2 and the inner function is u = x + 7.Differentiate outer function: Differentiate the outer function with respect to the inner function u. The outer function is -u^2. Its derivative with respect to u is -2u.Differentiate inner function: Differentiate the inner function with respect to x. The inner function is u = x + 7. Its derivative with respect to x is 1, since the derivative of x is 1 and the derivative of a constant is 0.Apply chain rule multiplication: Apply the chain rule by multiplying the derivatives from Step 3 and Step 4. The derivative of y with respect to x is the product of the derivative of the outer function and the derivative of the inner function: dy/dx = -2u * 1.Substitute inner function: Substitute the inner function back into the derivative. Replace u with x + 7 in the derivative we found in Step 5: dy/dx = -2(x + 7).Simplify derivative: Simplify the derivative. The derivative simplifies to dy/dx = -2x - 14.

$y=-(x+7)^2-9$

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y=−(x+7)2−9y=-(x+7)^2-9y=−(x+7)2−9

$y=-(x+7)^2-9$